3.4.41 \(\int e^{-1-e^x-x+e^{3+\log ^x(12)} (16-8 x+x^2)} (-1-e^x+e^{3+\log ^x(12)} (-8+2 x+(16-8 x+x^2) \log ^x(12) \log (\log (12)))) \, dx\)

Optimal. Leaf size=26 \[ e^{-1-e^x+e^{3+\log ^x(12)} (-4+x)^2-x} \]

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Rubi [F]  time = 8.07, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int e^{-1-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \left (-1-e^x+e^{3+\log ^x(12)} \left (-8+2 x+\left (16-8 x+x^2\right ) \log ^x(12) \log (\log (12))\right )\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[E^(-1 - E^x - x + E^(3 + Log[12]^x)*(16 - 8*x + x^2))*(-1 - E^x + E^(3 + Log[12]^x)*(-8 + 2*x + (16 - 8*x
+ x^2)*Log[12]^x*Log[Log[12]])),x]

[Out]

-Defer[Int][E^(-1 - E^x + E^(3 + Log[12]^x)*(16 - 8*x + x^2)), x] - Defer[Int][E^(-1 - E^x - x + E^(3 + Log[12
]^x)*(16 - 8*x + x^2)), x] - 8*Defer[Int][E^(2 - E^x - x + E^(3 + Log[12]^x)*(16 - 8*x + x^2) + Log[12]^x), x]
+ 2*Defer[Int][E^(2 - E^x - x + E^(3 + Log[12]^x)*(16 - 8*x + x^2) + Log[12]^x)*x, x] + 16*Log[Log[12]]*Defer
[Int][E^(2 - E^x - x + E^(3 + Log[12]^x)*(16 - 8*x + x^2) + Log[12]^x)*Log[12]^x, x] - 8*Log[Log[12]]*Defer[In
t][E^(2 - E^x - x + E^(3 + Log[12]^x)*(16 - 8*x + x^2) + Log[12]^x)*x*Log[12]^x, x] + Log[Log[12]]*Defer[Int][
E^(2 - E^x - x + E^(3 + Log[12]^x)*(16 - 8*x + x^2) + Log[12]^x)*x^2*Log[12]^x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-e^{-1-e^x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )}-e^{-1-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )}+\exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) (-4+x) \left (2-4 \log ^x(12) \log (\log (12))+x \log ^x(12) \log (\log (12))\right )\right ) \, dx\\ &=-\int e^{-1-e^x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx-\int e^{-1-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx+\int \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) (-4+x) \left (2-4 \log ^x(12) \log (\log (12))+x \log ^x(12) \log (\log (12))\right ) \, dx\\ &=-\int e^{-1-e^x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx-\int e^{-1-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx+\int \left (2 \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) (-4+x)+\exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) (-4+x)^2 \log ^x(12) \log (\log (12))\right ) \, dx\\ &=2 \int \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) (-4+x) \, dx+\log (\log (12)) \int \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) (-4+x)^2 \log ^x(12) \, dx-\int e^{-1-e^x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx-\int e^{-1-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx\\ &=2 \int \left (-4 \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right )+\exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) x\right ) \, dx+\log (\log (12)) \int \left (16 \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) \log ^x(12)-8 \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) x \log ^x(12)+\exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) x^2 \log ^x(12)\right ) \, dx-\int e^{-1-e^x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx-\int e^{-1-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx\\ &=2 \int \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) x \, dx-8 \int \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) \, dx+\log (\log (12)) \int \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) x^2 \log ^x(12) \, dx-(8 \log (\log (12))) \int \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) x \log ^x(12) \, dx+(16 \log (\log (12))) \int \exp \left (2-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )+\log ^x(12)\right ) \log ^x(12) \, dx-\int e^{-1-e^x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx-\int e^{-1-e^x-x+e^{3+\log ^x(12)} \left (16-8 x+x^2\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 6.44, size = 26, normalized size = 1.00 \begin {gather*} e^{-1-e^x+e^{3+\log ^x(12)} (-4+x)^2-x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(-1 - E^x - x + E^(3 + Log[12]^x)*(16 - 8*x + x^2))*(-1 - E^x + E^(3 + Log[12]^x)*(-8 + 2*x + (16
- 8*x + x^2)*Log[12]^x*Log[Log[12]])),x]

[Out]

E^(-1 - E^x + E^(3 + Log[12]^x)*(-4 + x)^2 - x)

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fricas [A]  time = 0.70, size = 26, normalized size = 1.00 \begin {gather*} e^{\left ({\left (x^{2} - 8 \, x + 16\right )} e^{\left (\log \left (12\right )^{x} + 3\right )} - x - e^{x} - 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^2-8*x+16)*log(log(12))*exp(x*log(log(12)))+2*x-8)*exp(exp(x*log(log(12)))+3)-exp(x)-1)*exp((x^2
-8*x+16)*exp(exp(x*log(log(12)))+3)-exp(x)-x-1),x, algorithm="fricas")

[Out]

e^((x^2 - 8*x + 16)*e^(log(12)^x + 3) - x - e^x - 1)

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giac [A]  time = 0.57, size = 40, normalized size = 1.54 \begin {gather*} e^{\left (x^{2} e^{\left (\log \left (12\right )^{x} + 3\right )} - 8 \, x e^{\left (\log \left (12\right )^{x} + 3\right )} - x - e^{x} + 16 \, e^{\left (\log \left (12\right )^{x} + 3\right )} - 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^2-8*x+16)*log(log(12))*exp(x*log(log(12)))+2*x-8)*exp(exp(x*log(log(12)))+3)-exp(x)-1)*exp((x^2
-8*x+16)*exp(exp(x*log(log(12)))+3)-exp(x)-x-1),x, algorithm="giac")

[Out]

e^(x^2*e^(log(12)^x + 3) - 8*x*e^(log(12)^x + 3) - x - e^x + 16*e^(log(12)^x + 3) - 1)

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maple [B]  time = 0.15, size = 56, normalized size = 2.15

method	result	size
risch	\({\mathrm e}^{{\mathrm e}^{\left (\ln \relax (3)+2 \ln \relax (2)\right )^{x}+3} x^{2}-8 \,{\mathrm e}^{\left (\ln \relax (3)+2 \ln \relax (2)\right )^{x}+3} x -{\mathrm e}^{x}+16 \,{\mathrm e}^{\left (\ln \relax (3)+2 \ln \relax (2)\right )^{x}+3}-x -1}\)	\(56\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((x^2-8*x+16)*ln(ln(12))*exp(x*ln(ln(12)))+2*x-8)*exp(exp(x*ln(ln(12)))+3)-exp(x)-1)*exp((x^2-8*x+16)*exp
(exp(x*ln(ln(12)))+3)-exp(x)-x-1),x,method=_RETURNVERBOSE)

[Out]

exp(exp((ln(3)+2*ln(2))^x+3)*x^2-8*exp((ln(3)+2*ln(2))^x+3)*x-exp(x)+16*exp((ln(3)+2*ln(2))^x+3)-x-1)

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maxima [B]  time = 1.74, size = 55, normalized size = 2.12 \begin {gather*} e^{\left (x^{2} e^{\left ({\left (\log \relax (3) + 2 \, \log \relax (2)\right )}^{x} + 3\right )} - 8 \, x e^{\left ({\left (\log \relax (3) + 2 \, \log \relax (2)\right )}^{x} + 3\right )} - x - e^{x} + 16 \, e^{\left ({\left (\log \relax (3) + 2 \, \log \relax (2)\right )}^{x} + 3\right )} - 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x^2-8*x+16)*log(log(12))*exp(x*log(log(12)))+2*x-8)*exp(exp(x*log(log(12)))+3)-exp(x)-1)*exp((x^2
-8*x+16)*exp(exp(x*log(log(12)))+3)-exp(x)-x-1),x, algorithm="maxima")

[Out]

e^(x^2*e^((log(3) + 2*log(2))^x + 3) - 8*x*e^((log(3) + 2*log(2))^x + 3) - x - e^x + 16*e^((log(3) + 2*log(2))
^x + 3) - 1)

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mupad [B]  time = 0.60, size = 45, normalized size = 1.73 \begin {gather*} {\mathrm {e}}^{-x}\,{\mathrm {e}}^{-8\,x\,{\mathrm {e}}^3\,{\mathrm {e}}^{{\ln \left (12\right )}^x}}\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{-{\mathrm {e}}^x}\,{\mathrm {e}}^{x^2\,{\mathrm {e}}^3\,{\mathrm {e}}^{{\ln \left (12\right )}^x}}\,{\mathrm {e}}^{16\,{\mathrm {e}}^3\,{\mathrm {e}}^{{\ln \left (12\right )}^x}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(exp(exp(x*log(log(12))) + 3)*(x^2 - 8*x + 16) - exp(x) - x - 1)*(exp(x) - exp(exp(x*log(log(12))) + 3
)*(2*x + exp(x*log(log(12)))*log(log(12))*(x^2 - 8*x + 16) - 8) + 1),x)

[Out]

exp(-x)*exp(-8*x*exp(3)*exp(log(12)^x))*exp(-1)*exp(-exp(x))*exp(x^2*exp(3)*exp(log(12)^x))*exp(16*exp(3)*exp(
log(12)^x))

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x**2-8*x+16)*ln(ln(12))*exp(x*ln(ln(12)))+2*x-8)*exp(exp(x*ln(ln(12)))+3)-exp(x)-1)*exp((x**2-8*x
+16)*exp(exp(x*ln(ln(12)))+3)-exp(x)-x-1),x)

[Out]

Timed out

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